To find the velocity of a ball thrown upward when the initial height, final height, and time are known, you can use the principles of projectile motion and the equations of motion.
The key equation to use in this case is the equation for vertical displacement in free fall:
h = v₀t - (1/2)gt²
where:
- h is the vertical displacement (final height - initial height),
- v₀ is the initial vertical velocity,
- t is the time taken,
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
Given the initial height (h₀), final height (h), and time (t), we can rearrange the equation to solve for the initial vertical velocity (v₀):
v₀ = (h - h₀ + (1/2)gt²) / t
Substituting the known values, you can find the velocity of the ball. It's important to note that the sign of the velocity will depend on the convention used. If upward is considered positive, the velocity will be positive if the ball is thrown upward and negative if it is thrown downward. Conversely, if downward is considered positive, the velocity will be negative when the ball is thrown upward and positive when it is thrown downward.